Networks with nearly identical degree distributions can place their hubs in sharply different neighborhoods. We develop a model diagnostic based on the mean degree of the neighbors of a degree-$k$ vertex. Under rank-one inhomogeneous random graphs, this statistic has degree-invariant centering and $k^{-1/2}$ fluctuations. Under non-rank-one kernels, posterior uncertainty about the root type can instead determine both centering and scale. Under linear preferential attachment, the statistic grows as $(m+\delta)\log k$. We turn these model-specific limits into goodness-of-fit tests for specified sparse-graph nulls and a weighted log-degree slope test for residual hub-neighborhood trends. Simulations evaluate null calibration, degree-distribution misspecification, and power against degree-matched preferential-attachment alternatives. Applications to high-school contact and arXiv coauthorship networks show that the method separates level misspecification from disassortative and positive residual trends. Reddit interaction networks provide a further appendix example.
A continuum of degree-normalized spectral embeddings that includes these commonly used choices as special cases is studied, and a row-wise central limit theorem is established under a random dot product graph model for this family of embeddings.
We prove recurrence criteria for inhomogeneous long-range percolation in dimensions one and two. In dimension one, recurrence follows from a purely geometric scarcity condition: long edges eventually disappear on exponential scales. This applies to weight-dependent random connection models and related one-dimensional s...
Johannes Bäumler, Lukas Lüchtrath, C. Mönch· 0 citations
This work extends Preferential attachment (PA) to spatial co-movement through a directed PA model whose out- and in-node weights follow temporally persistent Gaussian-process lognormal fields, and derives a strictly concave inverse that recovers the in-weights from terminal degree proportions.
We study the spectrum of the adjacency matrix $A_n$ of directed inhomogeneous random graphs on $n$ vertices. We assume that $A_n$ has independent entries and diverging average degree scale $s_n$. This framework includes, as special cases, the directed Chung--Lu random graph and directed stochastic block models. Assumin...
Experimental results on both synthetic and real-world HoMLN datasets demonstrate that the heuristics achieve accuracy comparable to the ground truth while significantly improving computational efficiency, thereby establishing the scalability and effectiveness of the HoMLN algorithms developed using the decoupling appro...
A. Ayowole-Obi, Abhishek Santra, Sharma Chakravarthy· 0 citations
The Ramsey community number $r_\kappa$ is the smallest network size at which a graph is better described by a partition into communities than by no partition, under a prescribed detection rule. On a scale-free graph this question is confounded: a block model can split the network merely to absorb its degree distributio...
Alexei Vazquez· 1 citation· ⚡1
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
